Abstract
We analyze the structure of space-time focusing of spatially-chirped pulses using a technique where each frequency component of the beam follows its own Gaussian beamlet that in turn travels as a ray through the system. The approach leads to analytic expressions for the axially-varying pulse duration, pulse-front tilt, and the longitudinal intensity profile. We find that an important contribution to the intensity localization obtained with spatial-chirp focusing arises from the evolution of the geometric phase of the beamlets.
Highlights
Spatial and angular chirp in ultrafast optical systems is treated as a misalignment (e.g. [1] ), but recent work in nonlinear microscopy [2,3,4], micromachining [5, 6] and waveguide writing [7] has taken advantage of the special properties of these beams
When a beam that has transverse spatial chirp is focused with a lens or curved mirror, the axial intensity is strongly localized because the pulse duration is not its shortest until all frequency components are fully overlapped
The strong localization that results from this simultaneous space-time focusing (SSTF) is useful for multiphoton microscopy because it improves the axial resolution for wide-field imaging
Summary
Spatial and angular chirp in ultrafast optical systems is treated as a misalignment (e.g. [1] ), but recent work in nonlinear microscopy [2,3,4], micromachining [5, 6] and waveguide writing [7] has taken advantage of the special properties of these beams. To provide more insight into the nature of the spatio-temporal coupling and to allow generalization to other systems, we develop in this paper a flexible, intuitive technique that we call the double ABCD method. The ray angles calculated from the raytrace are used to modify the expression for the Gaussian beam, thereby incorporating the phase information correctly This method can accurately describe the spatio-temporal structure of propagating beams with spatial chirp. As part of this analysis, we derive a general approach to starting with a field that has a known Fresnel propagation on-axis and modifying it to include the effects of tilting its propagation direction at an angle to the optical axis.
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